PQRS is a square. So PQ = RS
Since X and Y are the mid-points of RS and PQ respectively,
The diagonal of the square SQ and XY bisect each other at O.
So XO = YO
In ΔSOX & ΔYOQ
XO = YO
(both are right angles)
Congruent triangles have equal area.
So ar(ΔSOX) = ar(ΔYOQ) (proved)